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<p>This paper utilizes a mathematical model based on the Atangana–Baleanu fractal-fractional derivative to investigate different epidemiological aspects of monkeypox virus infection. The goal is to evaluate the effects of treatment and vaccination on the transmission dynamics of the virus. Initially, the model utilizes integer-order nonlinear differential equations, integrating imperfect vaccination and treatment as control strategies within the human population. Subsequently, the model is reformulated using a fractal fractional-order derivative based on a power law to offer a more comprehensive insight into disease dynamics. Conditions are established for the basic reproduction number and equilibrium points, and the feasible region of the model is identified. Stability analysis of the endemic equilibrium is conducted using the Lyapunov function approach. The fixed-point method is used to explore the existence and uniqueness of solutions in the Atangana–Baleanu model with fractal-fractional derivative order. Additionally, the study examines Ulam–Hyer’s stability. The numerical scheme applies Lagrange’s interpolation polynomial, enabling precise model interpolation. We present numerical comparisons for various fractional and fractal orders to showcase the accuracy of our approach.</p>

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Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月10日

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  • Tharmalingam Gunasekar,
  • Shanmugam Manikandan,
  • Salma Haque,
  • Murgan Suba,
  • Nabil Mlaiki

摘要

This paper utilizes a mathematical model based on the Atangana–Baleanu fractal-fractional derivative to investigate different epidemiological aspects of monkeypox virus infection. The goal is to evaluate the effects of treatment and vaccination on the transmission dynamics of the virus. Initially, the model utilizes integer-order nonlinear differential equations, integrating imperfect vaccination and treatment as control strategies within the human population. Subsequently, the model is reformulated using a fractal fractional-order derivative based on a power law to offer a more comprehensive insight into disease dynamics. Conditions are established for the basic reproduction number and equilibrium points, and the feasible region of the model is identified. Stability analysis of the endemic equilibrium is conducted using the Lyapunov function approach. The fixed-point method is used to explore the existence and uniqueness of solutions in the Atangana–Baleanu model with fractal-fractional derivative order. Additionally, the study examines Ulam–Hyer’s stability. The numerical scheme applies Lagrange’s interpolation polynomial, enabling precise model interpolation. We present numerical comparisons for various fractional and fractal orders to showcase the accuracy of our approach.